Problem 7.50

จาก \(Σ\vec{F} = m\vec{a}\)

îĵĵ

\(Fcos\theta - Fsin\theta - mg = m\vec{a}\)

îĵ

\(\vec{a} =\frac{Fcos\theta}{m}-\frac{Fsin\theta  + mg}{m}\)

จาก\(\vec{s}=\vec{u}t+\frac{1}{2}\vec{a}t^{2}\)

îĵîĵ

\(x-y=(0)t+\frac{1}{2}(\frac{Fcos\theta}{m}-\frac{Fsin\theta  + mg}{m})t^{2}\)

îĵîĵ

\(x - y =\frac{t^{2}Fcos\theta}{2m}-\frac{t^{2}(Fsin\theta  + mg)}{2m}\)

\(\therefore y =\frac{t^{2}(Fsin\theta  + mg)}{2m}\)

และ \(x = \frac{t^{2}Fcos\theta}{2m}\)

\(\therefore \frac{y}{x}=\frac{\frac{t^{2}(Fsin\theta  + mg)}{2m}}{\frac{t^{2}Fcos\theta}{2m}}\)

\(=\frac{y}{x}\frac{Fsin\theta  + mg}{Fcos\theta}\;\blacksquare\)